Please post the contents of the emulog.txt file after the problem occurs. The file can be found in "My Documents\PCSX2\logs" for the installer version or in "PCSX2\logs" for the portable/binary version.

The game is programmed so that they stop just out of the screen and don't actually leave I thought? This is really where the characters would be if you were able to make the game output widescreen on console.

My thought would be an alternative widescreen patch; instead of extending the edges of the screen, why not bring in the top/bottom? You lose a bit of data, but assuming the 2D viewport is drawn separately and the hack can detect that, you can resize that and then you wouldn't see programming quirks like this... I know some people have suggested this kind of widescreen hack for problematic titles in Dolphin.